Nick Clegg joined Boris Johnson in calling for an extension of the display created by ceramic artist Paul Cummins and stage designer Tom Piper.

Clegg said during his weekly phone-in on LBC that the display had “really struck a chord” and hoped it would be extended for a short time at least. “It is speaking to something very profound in people, that people want to be connected to our history. They want to trace their own family’s history to this huge act of national self-sacrifice. These ceramic poppies have really symbolised that.”

But the Tower of London is declining to budge. A spokeswoman said the last day of the display would be Remembrance Day itself and following that they would be removed prior to them being sent to people who had purchased them. Another reason for not extending the display is that the poppies’ transience was part of the original artistic concept.

“We have been overwhelmed by the public support for Blood Swept Lands and Seas of Red, our installation of ceramic poppies in the moat at the Tower of London,” the Tower said in a statement. “It has always been intended that the poppies will be in place until 11 November 2014 and after this time they will be cleaned and sent out to all those that have purchased them. The transience of the installation is key to the artistic concept, with the dispersal of the poppies into hundreds of thousands of homes marking the final phase of this evolving installation.

“We are currently planning further ways in which the Tower of London will be marking the coming years of the centenary and the legacy of the poppies in the moat.”

It has been estimated that four million people will have visited the poppies – each representing a British fatality during the first world war – by the time they are removed on 12 November. The sheer size of the daily crowds has taken everyone by surprise.

Johnson called them “a global visitor attraction” and said he was keen to explore keeping it open for longer “to give as many people as possible the chance to glimpse something so incredible, while easing the pressure on numbers.”

It would take a remarkable climbdown by Tower officials for that to now happen.

As things stand, a team of 11,000 volunteers will remove them next Wednesday and they will be sent to the hundreds of thousands who spent £25 each for one of the poppies, with all the money going to six charities providing support to service personnel, veterans and their families.

Chancellor George Osborne announced that the government would waive VAT on the sale of the poppies, amounting to around £1m.

One beneficiary from the sale of the poppies, military charity SSAFA, backed the closure of the exhibition next week.

A spokeswoman said: “Its transience is part of the overall artistic concept. Given that around four million people are thought to have visited the poppies, we appreciate that Historic Royal Palaces now needs to fulfil its obligation to those who have bought a poppy, and thereby generously supported the charities who are benefiting from the proceeds of their sale.”

Piper responded at the weekend: “For me, it is the symbolism of the single poppy for a single life which has really transformed the public’s perception of the work. I think it is a remarkably good thing that it is so accessible. We should not be trying to create something that is difficult to understand.”